Fast Excitation and Photon Emission of a Single-Atom-Cavity System
J. Bochmann, M. Mücke, G. Langfahl-Klabes,∗ C. Erbel,† B. Weber, H. P. Specht, D. L. Moehring,‡ and G. Rempe
Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
(Dated: January 4, 2014)
arXiv:0806.2600v2 [quant-ph] 3 Dec 2008
We report on the fast excitation of a single atom coupled to an optical cavity using laser pulses
that are much shorter than all other relevant processes. The cavity frequency constitutes a control
parameter that allows the creation of single photons in a superposition of two tunable frequencies.
Each photon emitted from the cavity thus exhibits a pronounced amplitude modulation determined
by the oscillatory energy exchange between the atom and the cavity. Our technique constitutes a
versatile tool for future quantum networking experiments.
PACS numbers: 42.50.Pq, 32.80.Qk, 37.10.Gh, 42.50.Xa
Single atoms exchanging single optical photons are
likely to be the essential components for the processing of
information in distributed quantum networks [1]. Both
carriers of quantum information exhibit low decoherence
rates and high controllability for information stored, for
example, in the spin state of an atom and the polarization state of a photon. This fact has made it possible to
implement increasingly more complex quantum protocols
involving atom-photon entanglement [2, 3, 4, 5, 6]. These
experiments were performed in two different settings.
One employed single trapped ions or atoms in a free-space
radiation environment [2, 3, 4, 5]. Characteristic features
of these experiments were short laser pulses exciting the
atom and subsequent spontaneous emission of a single
photon. The second setting made use of an optical cavity to efficiently direct photon emission into a predefined
spatial mode [6]. Here, a vacuum-stimulated Raman adiabatic passage technique was employed, with the driving
laser pulse controlling the photon shape [7, 8, 9]. Further
research towards the deterministic entanglement of remote atoms, the teleportation of atomic qubit states, and
the demonstration of quantum repeaters [10] would benefit if the advantages of both settings could be combined
in one setup, with bandwidth-limited indistinguishable
photons [11] emitted into a well-defined spatio-temporal
mode with high efficiency [12].
In this letter, we report on the generation of single photons via short-pulse laser excitation of an atom coupled
to an optical cavity. The most intriguing feature of our
excitation scheme is that the wave packet of the emitted photon is governed by the spectrum of the coupled
atom-cavity system alone, independent of the excitation
pulse shape and frequency. In contrast to free-space emission [13], the coupled atom-cavity system evolves with a
coherent oscillatory energy exchange between the atom
and the cavity, damped by atomic and cavity decay. We
record the shape of the emitted single photon and investigate its dependence from the detuning of the cavity with
respect to the atom. The observed oscillatory behavior
is in excellent agreement with theory and illustrates the
fundamentals of cavity quantum electrodynamics at the
single particle level. Our technique further opens up new
FIG. 1: (a) 87 Rb atoms are trapped within the TEM00 mode
of the cavity at the intersection of a standing wave dipole trap
(λ = 1064 nm) and an intracavity dipole trap (λ = 785 nm,
also used for stabilizing the cavity length). Two resonant
beams at ±45◦ to the standing wave trap and perpendicular
to the cavity axis provide cooling and fast pulse excitation.
The cavity output is coupled to an optical fiber and guided to
the detection setup. SPCM: single photon counting module,
NPBS: non-polarizing beam splitter, λ/4: quarter-wave plate,
EOM: electro-optic modulator, MOT: magneto-optical trap.
(b) Measured cavity output photon stream of a single atom
with constant laser cooling. The standing wave trap is turned
on at t = 0 with two atoms trapped during the first 300 ms.
perspectives for shaping single-photon wave packets [14].
Our new apparatus (similar to that described in
[15, 16], see Figure 1) uses an optical cavity operating in the intermediate coupling regime with
(gmax , κ, γ)/2π = (5.0, 2.7, 3.0) MHz. Here, gmax denotes
the atom-cavity coupling constant averaged over all Zeeman sublevels of the 87 Rb 5S1/2 F = 2 ↔ 5P3/2 F ′ = 3
transition for an atom at a field antinode, γ is the atomic
polarization decay rate, and κ is the cavity field decay
rate. The cavity is frequency-stabilized to this atomic
transition by means of a reference laser (λ = 785 nm),
which is itself locked to a frequency comb. The cavity
mirrors, each with 5 cm radius of curvature, are sepa-
2
rated by 495 µm giving a TEM00 -mode waist of 30 µm
and a finesse of 56000 (mirror transmissions 2 ppm and
101 ppm, total losses 10 ppm). The cavity output mode is
coupled into a single-mode optical fiber and directed to a
Hanbury Brown-Twiss photon detection setup consisting
of a non-polarizing beamsplitter and two single photon
counting modules. The detection efficiency for a single
photon present inside the cavity is ≈ 0.34, which includes
the directionality of the cavity output (≈ 0.9), spectral
separation from stabilization light and mode matching
into the fiber (≈ 0.85), and the efficiency of the detectors
(≈ 0.45).
Single 87 Rb atoms are loaded into the cavity mode
from a magneto-optical trap (MOT) via a running-wave
dipole trap beam (λ = 1064 nm) with a focus between
the MOT and the cavity [17]. When the atoms reach the
cavity, the transfer beam is replaced by a standing-wave
beam (λ = 1064 nm). This beam is focused at the cavity
mode and provides strong spatial confinement along its
axis (waist 16 µm, power 2.5 W, potential depth 3 mK).
Additionally, the atoms are confined along the cavity axis
by the 785 nm cavity reference laser (trap depth 70 µK).
Once trapped in the intra-cavity 2D optical lattice, the
atoms are exposed to a retro-reflected cooling laser beam
incident perpendicularly to the cavity axis. The cooling
beam is near resonant with the F = 2 ↔ F ′ = 3 transition (see below) and uses a lin⊥lin polarization configuration. Light resonant with the F = 1 ↔ F ′ = 2 transition
co-propagates with the cooling beam for optical pumping
out of the F = 1 ground state. A cavity emission signal
of a single atom trapped and cooled inside the cavity is
shown in Figure 1(b).
Long trapping times are observed under cavityenhanced cooling conditions over the range −70 MHz ≤
∆cool /2π ≤ −2 MHz while keeping (∆cav − ∆cool )/2π =
+5 MHz, where ∆cool and ∆cav are the detunings of
cooling laser and cavity with respect to the unperturbed
F = 2 ↔ F ′ = 3 atomic resonance. However, most important for this experiment, we are able to achieve trapping times of several seconds even outside the previously studied cavity-cooling regime [15]. This occurs,
for example, with a fixed cooling laser frequency at
∆cool /2π = −50 MHz and by varying the cavity frequency from −45 MHz ≤ ∆cav /2π ≤ +100 MHz. This
suggests that Sisyphus-like cooling [18] is the dominant
mechanism, with resulting atomic temperatures comparable to those measured in [15]. The advantage is now
that the cavity frequency is a free parameter while maintaining sufficiently long atom trapping times.
Fast excitation of the atom-cavity system is accomplished by switching off the cooling light and periodically driving the F = 2 ↔ F ′ = 3 transition with ≈ 3 ns
long laser pulses (FWHM). These pulses are created by
amplitude modulation of continuous-wave light using a
fiber-coupled electro-optic modulator (EOM, Jenoptik
model AM780HF). Due to the finite on:off ratio of the
FIG. 2: Histogram: normalized arrival time distribution of
photons emitted from the trapped atom-cavity system as a
function of time after the excitation pulse. Solid filled curve:
measured shape of the excitation pulse. Dotted line: exponential decay of the photon emission for an atom in free space.
Inset: Schematic of the atom-cavity system, excitation pulse,
and an emitted single photon.
EOM [19], we detune the center frequency of the excitation pulses from the cavity resonance by −30 MHz to suppress continuous-wave excitations [20]. Nevertheless, the
atom is still excited by the short pulse (measured bandwidth ∼ 200 MHz). Following the fast excitation, ideally
one photon will be produced because the laser pulse is
much shorter than the atomic lifetime (26 ns) and the
on-resonance build-up time for a field inside the cavity
(τfield ≈ π/2gmax = 50 ns). As the system is driven on
a cycling transition, no repumping is required before the
next excitation pulse. This scheme allows a pulse repetition rate of up to 5 MHz, limited by the duration of the
emitted single photon wave packet (. 200 ns). For all
measurements presented here, the pulse repetition rate
is 670 kHz.
Similar to the excitation of an atom in free space [13],
the fast laser pulse transfers the atom to the excited state
|ei. However, the atom-cavity state |e, n = 0i, where n
is the intracavity photon number, is not an eigenstate of
the coupled system. With atom and cavity tuned into
resonance, and for the moment neglecting dissipation,
the system exhibits oscillations according to
|Ψ(t)i = cos
Ωt
Ωt
|e, 0i + sin |g, 1i ,
2
2
(1)
where |gi is the atomic ground state and Ω = 2g is the
vacuum Rabi frequency [21]. This delays the peak of the
photon emission compared to an atom in free space, as
displayed in Fig. 2. For longer times, the oscillation is
damped out due to atomic and cavity decay resulting in
a smooth wave packet envelope.
The single-photon nature of this excitation scheme is
verified by a measurement of the intensity correlation
function g (2) (τ ) evaluated from photons arriving within
200 ns after the excitation pulse. We observe a high
3
FIG. 3: Measured arrival time distribution (dots) of photons
emitted from the cavity for different atom-cavity detunings
∆ac . The solid lines are numerical fits (see text).
suppression (90%) of coincidence events at time τ = 0
demonstrating that the protocol does indeed result in single photons. The remaining coincident detections come
from multiple trapped atoms (∼ 8%) and dark counts of
the photon detectors (∼ 2%). In contrast to free-space
emission [13], the probability of emitting two photons
from the atom-cavity system from one excitation pulse
is greatly suppressed (∼ 10−4 ) as the single-photon field
must first build up in the cavity before the photon can
be emitted.
Our measured probability of emitting a single photon
into the cavity mode following an excitation pulse is ∼ 8%
for ∆S = ∆cav = 80 MHz and ∆pulse = 50 MHz. Here
∆S denotes the atomic AC-Stark shift due to the dipole
trap, and ∆pulse is the detuning of the center frequency
of the excitation pulses (with respect to the unperturbed
F = 2 ↔ F ′ = 3 atomic transition). The photon production efficiency is limited by a number of technical difficulties. For instance, as the atom is not prepared in a well
defined initial Zeeman sublevel before each pulse, the average excitation probability saturates at ∼ 50% due to
the indeterminate transition strengths. Also, the average
photon decay probability into free space (∼ 80%) is a limitation since the atom-cavity cooperativity decreases due
to motion-induced variation of g. However, with appropriate choice and improvement of excitation and cavity
parameters, the photon emission efficiency can in principle approach unity [10, 13].
The shape of the emitted photon can be further controlled by applying a detuning between the Stark-shifted
atomic resonance and the cavity resonance ∆ac = ∆S −
∆cav [22]. The coupled system then oscillates between
the states |e, 0i and |g, 1i at a frequency
p
(2)
Ω′ = 4g 2 + ∆2ac .
Note that because γ ≈ κ, shifts of the oscillation frequency due to damping are negligible [21]. We observe
FIG. 4: Measured oscillation frequency of the emitted photons
(dots) as a function of ∆ac . The solid line shows the generalized Rabi frequency as a function of detuning from Eq. (2).
Inset: Normal modes of the coupled atom-cavity system.
these oscillations for a single atom trapped within a
standing wave, however, the position-dependent Stark
shift reduces the measured contrast. A more constant,
and in particular smaller, Stark shift is maintained in
a running-wave trap (∆S ≈ 2π × 17 MHz). We ensure
that less than one atom is present in the cavity at any
time by again measuring the g (2) (τ ) correlation function.
As seen in Fig. 3, the emitted photon wave packets exhibit modulations according to the population dynamics
of state |g, 1i. Note that no externally applied driving
field is present during the oscillations, and the measured
features are not due to many-photon or many-atom effects [23, 24, 25].
We find good agreement between the measured photon
wave packet shapes and an analytical model (solid lines
in Fig. 3). The model consists of an oscillating term for
the occupation of state |g, 1i and an exponential damping term due to atomic and cavity decay. Further, we
include the experimental shot-to-shot uncertainty of Ω′
using a Gaussian distribution of fixed width (10 MHz),
which accounts for position-dependent Stark shifts and
variations of g. We numerically fit this model to the data
and extract values of Ω′ as a function of atom-cavity detuning (Fig. 4). The extracted frequencies match well the
predicted hyperbolic function (Eq. 2) with a reduced chisquared χ2 = 1.13. These measurements can also be understood as time-domain normal-mode spectroscopy of a
coupled single-atom-cavity system in the optical regime.
In this interpretation, the observed modulation originates
from a quantum beat at the frequency difference between
the energy levels of the first pair of atom-cavity dressed
states (Fig. 4 inset) [26].
A complementary illustration of the coherent oscillations between the atom and the cavity is investigated by
pumping the system along the axis of the cavity (Fig. 5).
In this case, a weak 3 ns laser pulse excites the atom-
4
ing the frequency comb signal. This work was partially
supported by the Deutsche Forschungsgemeinschaft (Research Unit 635) and the European Union (IST program,
SCALA). G. L.-K. acknowledges support from the Rosa
Luxemburg Foundation. D. L. M. acknowledges support
from the Alexander von Humboldt Foundation.
∗
†
‡
FIG. 5: Measured photon arrival time distribution for excitation of the cavity with no atoms (filled dots) and . 1 atom
(histogram). The inset compares the temporal evolution of
state |g, 1i for transverse pumping (solid line) with that of
|e, 0i for cavity pumping (dashed line), illustrating the complementary dynamics.
[1]
[2]
[3]
[4]
[5]
[6]
cavity system such that when an output photon is detected, we know the system was in |g, 1i immediately
after excitation. We observe a deviation from a pure
exponential decay of the intra-cavity field as the energy
is temporarily stored in the atom. Quantitatively, we
can retrieve the temporal evolution of the population in
state |e, 0i by subtracting this signal from the exponential decay of the empty cavity at rate 2κ. The inset of
Fig. 5 compares this difference signal with the measured
evolution of |g, 1i from the experiment with transverse
excitation. The nearly identical time dependence of the
two signals testifies to the coherent exchange of energy
between atom and field.
In future experiments, by terminating the atom-cavity
oscillations with a suitably timed atomic de-excitation
pulse, the fast excitation technique should allow one to
design single photons with duration shorter than the system’s decay time [14]. This includes the possibility to
generate time-symmetric photons important for quantum networking [27]. Additionally, a single photon in
a superposition of two tunable frequencies, as demonstrated here, may be useful as a frequency qubit [28, 29].
Our scheme may also find application in the investigation of higher-lying dressed states in cavity QED systems
[30] and for the deterministic generation of multi-photon
Fock states [31]. Finally, our fast excitation technique
can improve existing atom-photon entanglement experiments [6] by reducing unwanted multiple-photon events,
and can be extended to multi-photon entanglement protocols [32].
The authors thank K. Murr for useful discussions and
B. Bernhard, T. Wilken and R. Holzwarth for provid-
[7]
[8]
[9]
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[11]
[12]
[13]
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[17]
[18]
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[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
Present address: Clarendon Laboratory, University of
Oxford, Parks Road, Oxford OX1 3PU, UK
Present address: Lehrstuhl für Energiesysteme, Technische Universität München, 85748 Garching, Germany
Electronic address: [email protected]
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